, JF 2005 Presented by: Rustom Irani, NYU Stern November 13, 2009
Outline 1 Motivation Production-Based Asset Pricing Framework 2 Assumptions Firm s Problem Equilibrium 3 Main Findings Mechanism Testable Implications 4 5 Firm Heterogeneity Figure 4 Other Directions?
Outline Motivation Production-Based Asset Pricing Framework 1 Motivation Production-Based Asset Pricing Framework 2 Assumptions Firm s Problem Equilibrium 3 Main Findings Mechanism Testable Implications 4 5 Firm Heterogeneity Figure 4 Other Directions?
What is the Value Premium? Motivation Production-Based Asset Pricing Framework Sort all stocks on basis of Book-to-Market (BM) ratio: Value stocks (e.g., GE?) have highest BM ratio; Growth stocks (e.g., Google?) have lowest BM ratio; Value has 6% higher average returns/yr vs. Growth; Value stocks derive value from assets-in-place, whereas Growth from growth options; How could assets-in-place riskier than growth options?
Some Numbers Motivation Production-Based Asset Pricing Framework Risk-return relation: E [R j R f ] = β j λ m β j measures quantity of risk: Higher β j implies greater covariance with market return; Asset pays off in good states; Bad for consumption-smoothing; λ m measures market price of risk: Reflects investor preferences; Idiosyncratic risk irrelevant. Figure: Low = Growth...Value returns are more correlated with market return!
Equilibrium (of the Supply-Side) Motivation Production-Based Asset Pricing Framework Industry equilibrium model with heterogeneous firms; Idiosyncratic (firm-level) and aggregate (economy-wide) productivity shocks to generate cross-section of returns: 1 Idiosyncratic shocks = firm-level heterogeneity; 2 Aggregate uncertainty = un-diversifiable risk in economy. Prices exogenous function of industry output; Cash-flows/returns are endogenously determined by firms characteristics!
s Story Motivation Production-Based Asset Pricing Framework 1 Asymmetric, costly reversibility of capital stock: Hampers dividend smoothing; Disinvesting in bad times more risky; 2 Counter-cyclical market risk premium; Increase market risk premium when Value looks riskiest;...makes assets-in-place look riskier than growth options, especially in bad times!
Outline Assumptions Firm s Problem Equilibrium 1 Motivation Production-Based Asset Pricing Framework 2 Assumptions Firm s Problem Equilibrium 3 Main Findings Mechanism Testable Implications 4 5 Firm Heterogeneity Figure 4 Other Directions?
Environment Assumptions Firm s Problem Equilibrium 1 Discrete time, infinite-horizon: Firms live forever, no bankruptcy, entry/exit, etc.; 2 Industry composed of a continuum of (stock price) value-maximizing firms that produce a homogenous product: Firms ex-ante identical; One-sector model; 3 Firms behave competitively, i.e., take industry price as given.
Technology Assumptions Firm s Problem Equilibrium Capital is only input in production: y jt = e xt+z jt k α jt : α (0, 1) = decreasing returns to scale; Two productivity shocks: 1 Aggregate: x t+1 = x(1 ρ x ) + ρ x x t + σ x ɛ x t+1 Average productivity in economy; 2 Idiosyncratic: z jt+1 = ρ z z jt + σ z ɛ z t+1 Orthogonal, firm-specific component; Shocks IID standard normal and independent of each other.
Stochastic Discount Factor Assumptions Firm s Problem Equilibrium No consumer side of economy, production side only; consumer s IMRS (firm s IMRT?) directly: log M t+1 = log ξ + γ t (x t x t+1 ) γ t = γ 0 + γ 1 (x t x) γ t is time-varying market price of x t risk: γ 1 < 0 = counter-cyclical price of aggregate risk; Aggregate productivity below trend, higher compensation for risk-taking; Habit or LRR interpretation valid?
Industry Demand Assumptions Firm s Problem Equilibrium Output price as function of industry output: P(Y t ) = Y η t Demand curve fixed and independent of state of economy; Industry output/price fluctuates with aggregate state and depends on the cross-sectional distribution of firms.
Asymmetric Adjustment Costs Assumptions Firm s Problem Equilibrium Asymmetric and quadratic capital adjustment costs; ( ) h(i jt, k jt ) 1 2 θ ijt 2 jt k kjt jt ; θ t θ + χ {ijt>0 }+θ χ {ijt<0 }; Higher per unit cost in contracting than expanding capital stocks (θ > θ + > 0).
Profits and Dividends Assumptions Firm s Problem Equilibrium π(k jt, z jt ; x t, P t ) = P t y jt f χ {yjt >0}; f is a nonnegative fixed cost of production; d jt π jt i jt h(i jt, k jt ); Firms are all-equity financed; What about holding cash?
Value Maximization Assumptions Firm s Problem Equilibrium Let v denote the market value of the firm: v(k jt, z jt ; x t, P t ) = max E t M τ d jτ i jt,k jt+1 τ=t Dynamic programming problem can be formulated as: v(k jt, z jt ; x t, P t ) = max i jt {d jt + E t [M t+1 v jt+1 ]} s.t. k jt+1 = i jt + (1 δ)k jt z jt+1 = ρ z z jt + σ z ɛ z t+1 x t+1 = x(1 ρ x ) + ρ x x t + σ x ɛ x t+1 P t+1 = Ω (P t, x t, x t+1 ) M t+1 = βe γt(xt x t+1)
Beta Pricing Assumptions Firm s Problem Equilibrium Risk-return relation: E t [R jt+1 R ft ] = β jt λ mt R jt+1 v jt+1 /(v jt d jt ) R ft = 1/E t [M t+1 ] = β 1 e (1 ρx )σmt(xt x) 1 2 σ2 mt ( ) λ mt Var t [M t+1 ] /E t [M t+1 ] = e 1 2 σ2 mt e 1 2 σ2 mt 1 σ mt σ x γ t β jt Cov t [R jt+1, M t+1 ] /Var t [M t+1 ]
Equilibrium Assumptions Firm s Problem Equilibrium A recursive competitive equilibrium is an industry price, investment and value functions for the firm, and a law of motion for the cross-sectional distribution of firms {P, i, v, Γ } s.t.: 1 Optimality: Given prices, i (k t, z t ; x t, P t ) solves the firm s value-maximization problem and v (k t, z t ; x t, P t ) is the associated value function; 2 Market Clearing: P t = Y η t ; 3 Aggregate Consistency: The LOM for the cross-sectional firm distribution, µ t+1 = Γ (µ t, x t, x t+1 ), is consistent with optimal firm behavior.
Outline Main Findings Mechanism Testable Implications 1 Motivation Production-Based Asset Pricing Framework 2 Assumptions Firm s Problem Equilibrium 3 Main Findings Mechanism Testable Implications 4 5 Firm Heterogeneity Figure 4 Other Directions?
Calibration and Main Findings Mechanism Testable Implications Some kind of calibration to match time-series moments of interest rates and various market returns; I m not going to discuss this... Implied cross-sectional returns (BM portfolio means, variances and market betas) consistent with the data; Argue that both counter-cyclical market price of risk and costly capital reversal essential ingredients.
Main Findings Mechanism Testable Implications Profitability, Productivity and Value The only source of heterogeneity is the firm-level productivity shock; Growth corresponds to: 1 High individual productivity; 2 High profitability; Figure: Value ( Growth ) portfolio corresponds to top (bottom) 30% of book-to-market ratios. Vice versa for Value.
Main Findings Mechanism Testable Implications Investment Over the Business Cycle All firms invest in good times; Growth firms (nearly) always invest and grow faster than Value firms; Value firms disinvest in bad times; How does Value and capital stock line up?
Main Findings Mechanism Testable Implications Productivity, Flexibility and the Value Premium 1 Costly reversibility of capital stock: Prevents dividend smoothing by firms; In bad times, Value firms will be disinvesting; If hit by another bad agg. shock, Value firms face even steeper adjustment costs, further decreasing their dividends/returns; Hence, Value dividends/returns co-vary more closely with economic downturns, making them look more risky; In good times, negligible dispersion of risk (β Value β Growth ). 2 Counter-cyclical market risk premium: Market price of risk increases precisely when the dispersion of risk is maximized!
Main Findings Mechanism Testable Implications Using to Motivate Empirical Work This is a single-sector partial equilibrium model; uses results from model to motivate empirical analysis; No (worthwhile) empirical analysis in this paper.
Predictability of Value Premium Main Findings Mechanism Testable Implications 1 Value spread (BM H BM L ) predicts Value Premium; 2 Value Premium is countercyclical: Negatively correlated with aggregate productivity shock; Why are results so weak at monthly frequency? Figure: R t+1 (Value Growth) = βx t + ɛ t+1 from monthly simulation.
Main Findings Mechanism Testable Implications Eqm Effects and Industry Returns Predictability In equilibrium, the cross-sectional distribution of firms over state-space affects the LOM for prices, thus firms value; Firm-level risk irrelevant, but distn across firms important; Goyal & Santa-Clara ( Idiosyncratic Risk Matters!, 2003): predicts x-sectional return vol forecasts market return; Consistent with empirical evidence in GS.
Outline 1 Motivation Production-Based Asset Pricing Framework 2 Assumptions Firm s Problem Equilibrium 3 Main Findings Mechanism Testable Implications 4 5 Firm Heterogeneity Figure 4 Other Directions?
1 Equilibrium model of asset pricing linking behavior of risk and returns to fundamentals of the real economy; 2 Heterogeneity arises from idiosyncratic productivity shocks; Value corresponds to low productivity; 3 Excess capacity in downturns hampers dividend smoothing; 4 Countercyclical market risk premium exacerbates effect; 3 & 4 both make sense; 5 Matches important moments including Value Premium; 6 Rich set of testable implications.
Outline Firm Heterogeneity Figure 4 Other Directions? 1 Motivation Production-Based Asset Pricing Framework 2 Assumptions Firm s Problem Equilibrium 3 Main Findings Mechanism Testable Implications 4 5 Firm Heterogeneity Figure 4 Other Directions?
Understanding Firm-Level Risk Firm Heterogeneity Figure 4 Other Directions? This is a model of lucky firms versus unlucky firms: All firms are ex-ante identical; Some firms are Value, others Growth depending on luck; Given Stationarity, luck will eventually wear off; Value will eventually become growth and vice versa; Value has unused capital because used to be productive; I find this rather unsatisfactory... In the data, do firms cycle between Growth/Value status? Or is there something non-stationary going on? A firm life-cycle?
Value in the Data? Firm Heterogeneity Figure 4 Other Directions? Do Value stocks actually correspond to low productivity firms in the data? If this is not the case then model does not make any sense; Bazdresch et al. (WP, 2009) side-step issue: We do not observe firm-level productivity; We do observe investment rates; Sort firms on the basis of investment rates.
Firm Heterogeneity Figure 4 Other Directions? Estimating Firm-Level Productivity Risk has common, exogenous firm-level productivity spec.; Bachman & Bayer (WP, 2009) actually estimate firm-level Solow residuals using German data; Phillipon & Franco (REStat, 2007) does something similar;
Firm Heterogeneity Figure 4 Other Directions? Estimating Firm-Level Productivity Risk has common, exogenous firm-level productivity spec.; Bachman & Bayer (WP, 2009) actually estimate firm-level Solow residuals using German data; Phillipon & Franco (REStat, 2007) does something similar; 1 BB find that firm-level productivity risk is time-varying and correlated with aggregate shocks. This model? Constant variance of prod. shocks assumed; Agg. prod. innovations affect all firms the same way; How does x-sectional distn (µ t ) vary over business cycle (x t )? 2 Estimate production function for each firm (or different BM deciles) and see if Value and firm-level risk really do line up?
Firm Heterogeneity Figure 4 Other Directions? Other Forms of Firm-Level Heterogeneity? 1 Financing frictions (Gomes, Yaron &, RFS, 2006): Time-varying costs of issuing debt and equity. 2 What about distress risk in neoclassical framework? Allow firms to endogenously default in this model? Would need bond issuance by firm. Very weak empirical evidence (Campbell et al., JF, 2008); 3 Other characterizations? Generating ideas (Kogan & Papanikolaou, WP, 2009); Durability of product (Gomes, Kogan & Yogo, JPE, 2009).
Firm Heterogeneity Figure 4 Other Directions? Interpreting Figure 4: A Peso Problem? Large expected Value Premium consistent with Value Spread of 16, a 2.5 stdev event in model. Figure: Value Spread and Premium over the business cycle.
And in the Data? Firm Heterogeneity Figure 4 Other Directions? Value Spread 5 in data, never equals 16 in-sample; Should I interpret this as a Peso problem? Figure: Log BM series for Value/Growth Firms (Cohen et al., JF, 2003).
More Data Qs Firm Heterogeneity Figure 4 Other Directions? What does the distribution of the Value Spread look like in the data? How has this distribution changed over time and with the business cycle? This model has a counter-cyclical Value Spread; What about other equilibrium models?
Firm Heterogeneity Figure 4 Other Directions? Figure 4 Again: Where s 3? Where is the model with symmetric adjustment cost and counter-cyclical market price of risk??? Suspect, given the results in Bazdresch et al. (WP, 2009); Why not impose symmetric adjustment cost and structural estimate remaining parameters?
Firm Heterogeneity Figure 4 Other Directions? A Bit More of a Corporate Flavor... Another awfully titled paper Anomalies (Li et al., RFS, 2008) documents empirical evidence: 1 Dividends highly persistent; 2 Payout policy between equity and bond holders: New equity share (negatively) predicts future returns (Baker & Wurgler, JF, 2000); New debt issuance has smaller negative impact; Positive stock-price drift follows payout to shareholders but not payout to bondholders. Extend current model to include: 1 Payout policy and trade-off between dividends and share repurchases; 2 Incorporate a defaultable bond and consider debt/equity policy.